Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22549902 | C2 | direct (N × H) |
| 4. C2×Dic127⋊C8 | C2 | semidirect |
| 14. Dic127⋊C8 | C22 | semidirect |
| 66. C2×C127 | #424 | semidirect |
| 70. C127 | C2×#424 | semidirect |
| 136. C2 | #22549902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523232 | 2 |
| C2×#16861168 | 2 |
| #22549902 | 2 |
| C2×Dic127⋊C8 | 2 |
| C23×C8×C127 | 2 |
| C2×#424 | 127 |